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Iterative Solution of Large Sparse Systems of Equations

  • Wolfgang Hackbusch

Part of the Applied Mathematical Sciences book series (AMS, volume 95)

Table of contents

  1. Front Matter
    Pages i-xxiii
  2. Linear Iterations

    1. Front Matter
      Pages 1-2
    2. Wolfgang Hackbusch
      Pages 3-16
    3. Wolfgang Hackbusch
      Pages 17-34
    4. Wolfgang Hackbusch
      Pages 89-122
    5. Wolfgang Hackbusch
      Pages 123-136
    6. Wolfgang Hackbusch
      Pages 137-172
  3. Semi-Iterations and Krylov Methods

    1. Front Matter
      Pages 173-174
    2. Wolfgang Hackbusch
      Pages 175-209
    3. Wolfgang Hackbusch
      Pages 211-228
    4. Wolfgang Hackbusch
      Pages 229-262
  4. Special Iterations

    1. Front Matter
      Pages 263-264
    2. Wolfgang Hackbusch
      Pages 265-324
    3. Wolfgang Hackbusch
      Pages 325-370
    4. Wolfgang Hackbusch
      Pages 371-384
    5. Wolfgang Hackbusch
      Pages 385-400
  5. Back Matter
    Pages 401-509

About this book

Introduction

In the second edition of this classic monograph, complete with four new chapters and updated references, readers will now have access to content describing and analysing classical and modern methods with emphasis on the algebraic structure of linear iteration, which is usually ignored in other literature.

The necessary amount of work increases dramatically with the size of systems, so one has to search for algorithms that most efficiently and accurately solve systems of, e.g., several million equations. The choice of algorithms depends on the special properties the matrices in practice have. An important class of large systems arises from the discretization of partial differential equations. In this case, the matrices are sparse (i.e., they contain mostly zeroes) and well-suited to iterative algorithms.

The first edition of this book grew out of a series of lectures given by the author at the Christian-Albrecht University of Kiel to students of mathematics. The second edition includes quite novel approaches.

Keywords

Analysis Iterative Solution Methods Multigrid Method Matrices Nonlinear Equations Tensor-based Methods

Authors and affiliations

  • Wolfgang Hackbusch
    • 1
  1. 1.Max Planck Institute for Mathematics inLeipzigGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-28483-5
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-28481-1
  • Online ISBN 978-3-319-28483-5
  • Series Print ISSN 0066-5452
  • Series Online ISSN 2196-968X
  • Buy this book on publisher's site
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